# Jacobian math homework

1. Mar 12, 2010

### phrygian

1. The problem statement, all variables and given/known data

Suppose that P, Q, and R are regions in R2, and suppose T1 : P -> Q and T2 : Q -> R are
dierentiable. Use the (multivariable) Chain Rule and det(AB) = det(A)det(B) to show that the Jacobian of the
composition T2 o T1 is the product of the Jacobians of T1 and T2.

2. Relevant equations

3. The attempt at a solution

So if I say T1 is given by x = g(u,v) and y = h(u,v) and T2 is given by u = i(s,t) and v = j(s,t) , I know how to find the two jacobians T1 and T2 but am confused how do you find the jacobian of the composite transformation T1 o T2?

2. Mar 12, 2010

### ystael

Re: Jacobian

Follow their instructions: use the chain rule to compute the derivative of $$T_2 \circ T_1$$.

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